Ron Guth: The Draped Bust design that first appeared on large cents in 1796 did not appear on half cents until 1800. Fortunately for collectors, the inaugural year of the type (1800) is a reasonably common date. The 1802, the first overdate of any half cent, is the rarest date of the type and includes one variety with a new reverse (scarce) and another with the old reverse of 1800 (extremely scarce). All other dates of this type are common, although there are some interesting and valuable varieties to excite the collector. The 1804 "Spiked Chin" was caused when a foreign object was impressed into the obverse die, creating a spear-like projection from Liberty's chin. 1804 half cents are also found with either a Plain 4 (no crosslet) or a Crosslet 4, and with or without stems on the reverse. 1805 and 1806 half cents are found in some combination of Small and Large final digits in the date and/or with or without stems. The 1808/7 is the other overdate of this type. As with most early U.S. coins, high grade examples of Draped Bust half cents are hard to find, but several hoards and mini-hoards of 1800 and 1806 half cents have made the task easier. Full red Uncirculated examples are extremely rare and, for most dates, simply don't exist.
Sources and/or recommended reading:"Walter Breen's Encyclopedia of United States Half Cents 1793-1857" by Walter Breen
"American Half Cents - The 'Little Half Sisters' (Second Edition)" by Roger S. Cohen, Jr.